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f11c7a6bbf5754fee116b638d99a33a6
Omni-MATH_pascal
math
Number Theory
We call the pair $(m, n)$ of positive integers a happy pair if the greatest common divisor of $m$ and $n$ is a perfect square. For example, $(20, 24)$ is a happy pair because the greatest common divisor of 20 and 24 is 4. Suppose that $k$ is a positive integer such that $(205800, 35k)$ is a happy pair. What is the numb...
Suppose that $(205800, 35k)$ is a happy pair. We find the prime factorization of 205800: $205800 = 2^3 \times 3^1 \times 5^2 \times 7^3$. Note also that $35k = 5^1 \times 7^1 \times k$. Let $d$ be the greatest common divisor of 205800 and $35k$. We want to find the number of possible values of $k \leq 2940$ for which $...
30
Let's tackle this problem step by step. we need to find the number of positive integers \( k \) with \( k \leq 2940 \) such that the pair \( (205800, 35k) \) is a "happy pair." a happy pair is defined as a pair where the greatest common divisor (gcd) of the two numbers is a perfect square. first, let's understand what...
[{'start': 1, 'end': 3, 'description': 'Introduction and understanding the condition for a happy pair', 'content': 'Let\'s tackle this problem step by step. we need to find the number of positive integers \\( k \\) with \\( k \\leq 2940 \\) such that the pair \\( (205800, 35k) \\) is a "happy pair." a happy pair is def...
section1: Let's tackle this problem step by step. we need to find the number of positive integers \( k \) with \( k \leq 2940 \) such that the pair \( (205800, 35k) \) is a "happy pair." a happy pair is defined as a pair where the greatest common divisor (gcd) of the two numbers is a perfect square. first, let's under...
[{'section_number': 1, 'strategy_shift': '0', 'strategy_shift_step': '', 'reasoning_usefulness': '1', 'reasoning_correctness': '0', 'error_step': '', 'explanation': '', 'correction': '', 'reflection': '0', 'reflection_start_step': ''}, {'section_number': 2, 'strategy_shift': '1', 'strategy_shift_step': '4', 'reasoning_...
0
[2]
[]
[7]
[]
676adb9206bdd7cd09a9a20abec112da
Omni-MATH_HMMT_11
math
Number Theory
Call a number feared if it contains the digits 13 as a contiguous substring and fearless otherwise. (For example, 132 is feared, while 123 is fearless.) Compute the smallest positive integer $n$ such that there exists a positive integer $a<100$ such that $n$ and $n+10 a$ are fearless while $n+a, n+2 a, \ldots, n+9 a$ a...
First of all, note that we cannot have $n, n+a, \ldots, n+10 a$ be less than 1000, since we cannot have fearless numbers have 13 as their last two digits since $a<100$, and $129,130,131, \ldots, 139$ doesn't work as 139 is feared. Thus, we must utilize numbers of the form $13 x y$, where $1,3, x$, and $y$ are digits. I...
1287
Let's tackle this problem step by step. it's a bit tricky, but i think if i break it down, i can figure it out. first, i need to understand what a "feared" and "fearless" number is. a number is feared if it contains the digits "13" in a row, like 132 or 313. if it doesn't have "13" together, it's fearless, like 123 or...
[{'start': 1, 'end': 2, 'description': 'Define "feared" and "fearless" numbers and set up the problem conditions', 'content': 'Let\'s tackle this problem step by step. it\'s a bit tricky, but i think if i break it down, i can figure it out.\n\nfirst, i need to understand what a "feared" and "fearless" number is. a numb...
section1: Let's tackle this problem step by step. it's a bit tricky, but i think if i break it down, i can figure it out. first, i need to understand what a "feared" and "fearless" number is. a number is feared if it contains the digits "13" in a row, like 132 or 313. if it doesn't have "13" together, it's fearless, l...
[{'section_number': 1, 'strategy_shift': '0', 'strategy_shift_step': '', 'reasoning_usefulness': '1', 'reasoning_correctness': '0', 'error_step': '', 'explanation': '', 'correction': '', 'reflection': '0', 'reflection_start_step': ''}, {'section_number': 2, 'strategy_shift': '0', 'strategy_shift_step': '', 'reasoning_u...
0
[3, 5, 6]
[]
[7]
[]
17af0b1210d442d79a4a9a512102eab0
Omni-MATH_HMMT_11
math
Number Theory
"A number $n$ is $b a d$ if there exists some integer $c$ for which $x^{x} \\equiv c(\\bmod n)$ has (...TRUNCATED)
"Call a number good if it is not bad. We claim all good numbers are products of distinct primes, non(...TRUNCATED)
25
"So i'm trying to solve this problem about \"bad\" integers. the definition given is that a number \(...TRUNCATED)
"[{'start': 1, 'end': 5, 'description': 'Introduction to the problem of identifying \"bad\" integers(...TRUNCATED)
"section1: So i'm trying to solve this problem about \"bad\" integers. the definition given is that (...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '0', 'strategy_shift_step': '', 'reasoning_usefulness': '1(...TRUNCATED)
0
[2]
[]
[2]
[]
15b7ef6c3f5ca4ec9900c20e585c7e15
Omni-MATH_HMMT_2
math
Number Theory
"Our next object up for bid is an arithmetic progression of primes. For example, the primes 3,5, and(...TRUNCATED)
12. We can get 12 with 110437 and difference 13860.
12
"Alright, so I've got this problem here: I need to find the largest possible length of an arithmetic(...TRUNCATED)
"[{'start': 1, 'end': 3, 'description': 'Introduction to the problem and understanding the concept o(...TRUNCATED)
"section1: Alright, so I've got this problem here: I need to find the largest possible length of an (...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '0', 'strategy_shift_step': '', 'reasoning_usefulness': '1(...TRUNCATED)
0
[3, 5, 6, 11, 12, 13, 15, 17, 19]
[]
[14]
[8, 12, 14, 18]
d5bbdb2d68e9123f5953cd893bdbc7cc
Omni-MATH_HMMT_2
math
Number Theory
"Estimate the number of positive integers $n \\leq 10^{6}$ such that $n^{2}+1$ has a prime factor gr(...TRUNCATED)
"Let $N$ denote $10^{6}$. We count by summing over potential prime factors $p$. For any prime $p>2$,(...TRUNCATED)
757575
"So i've got this problem: i need to estimate the number of positive integers \\( n \\leq 10^6 \\) s(...TRUNCATED)
"[{'start': 1, 'end': 2, 'description': 'Introduction and interpretation of the problem', 'content':(...TRUNCATED)
"section1: So i've got this problem: i need to estimate the number of positive integers \\( n \\leq (...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '1', 'strategy_shift_step': '1', 'reasoning_usefulness': '(...TRUNCATED)
0
[1, 3, 6, 7, 9, 10, 12, 14, 16]
[]
[16]
[5, 6, 8]
869cb794265bf3b61c121e9cba8e7b01
Omni-MATH_HMMT_2
math
Number Theory
"For positive integers $a$ and $b$, let $M(a, b)=\\frac{\\operatorname{lcm}(a, b)}{\\operatorname{gc(...TRUNCATED)
"The desired condition is that $x_{n}=5 x_{n+1}$ or $x_{n+1}=5 x_{n}$. Note that for any prime $p$, (...TRUNCATED)
20
"Let's tackle this problem step by step. it's a bit involved, but if i break it down, i think i can (...TRUNCATED)
"[{'start': 1, 'end': 3, 'description': 'Introduction and understanding the recursive sequence', 'co(...TRUNCATED)
"section1: Let's tackle this problem step by step. it's a bit involved, but if i break it down, i th(...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '1', 'strategy_shift_step': '1', 'reasoning_usefulness': '(...TRUNCATED)
0
[1, 2, 8, 9, 14, 15, 18]
[]
[2, 18]
[3, 8, 13]
0e6edffc986c155d78e80be684cc7582
Omni-MATH_imo
math
Number Theory
"Let $ p$ be an odd prime number. How many $ p$-element subsets $ A$ of $ \\{1,2,\\dots,2p\\}$ are t(...TRUNCATED)
"Let \\( p \\) be an odd prime number. We are tasked with finding the number of \\( p \\)-element su(...TRUNCATED)
\boxed{2 + \frac{1}{p} \left(\binom{2p}{p} - 2 \right)}
"So i have this problem: let \\( p \\) be an odd prime number. how many \\( p \\)-element subsets \\(...TRUNCATED)
"[{'start': 1, 'end': 5, 'description': 'Introduction to the problem and initial approach', 'content(...TRUNCATED)
"section1: So i have this problem: let \\( p \\) be an odd prime number. how many \\( p \\)-element (...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '1', 'strategy_shift_step': '2', 'reasoning_usefulness': '(...TRUNCATED)
0
[1, 2]
[]
[2]
[]
cd48db5fd3ebb985ad433d2d2dbc2414
Omni-MATH_HMMT_11
math
Number Theory
"Let $n$ be the answer to this problem. Find the minimum number of colors needed to color the diviso(...TRUNCATED)
"We first answer the following question. Find the minimum number of colors needed to color the divis(...TRUNCATED)
50
"So i'm trying to solve this problem, but it's a bit tricky. let's see what it's asking for. the pro(...TRUNCATED)
"[{'start': 1, 'end': 3, 'description': 'Initial problem interpretation and formulation', 'content':(...TRUNCATED)
"section1: So i'm trying to solve this problem, but it's a bit tricky. let's see what it's asking fo(...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '1', 'strategy_shift_step': '3', 'reasoning_usefulness': '(...TRUNCATED)
0
[1, 5, 8]
[9]
[9]
[3, 5, 6, 8, 9]
812440be8d0faf8f2fd9e93dce5b8eb3
Omni-MATH_pascal
math
Number Theory
"In the subtraction shown, $K, L, M$, and $N$ are digits. What is the value of $K+L+M+N$?\\n$$\\begi(...TRUNCATED)
"We work from right to left as we would if doing this calculation by hand. In the units column, we h(...TRUNCATED)
17
"So i've got this subtraction problem here:\n\n??6 k 0 l \n-??m 9 n 4 \n=?2011\n\nand i need to fi(...TRUNCATED)
"[{'start': 1, 'end': 2, 'description': 'Introduction to the subtraction problem and initial setup',(...TRUNCATED)
"section1: So i've got this subtraction problem here:\n\n??6 k 0 l \n-??m 9 n 4 \n=?2011\n\n\nsect(...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '0', 'strategy_shift_step': '', 'reasoning_usefulness': '1(...TRUNCATED)
0
[4, 5, 8, 12]
[5]
[12]
[]
3fdbdd7575ff5ff47b72ccf60fca8704
OlympiadBench
math
Number Theory
"Let $\\mathcal{S}$ be the set of integers from 0 to 9999 inclusive whose base- 2 and base- 5 repres(...TRUNCATED)
"[\"The remainders of an integer $N$ modulo $2^{4}=16$ and $5^{4}=625$ uniquely determine its remain(...TRUNCATED)
['6248']
"Let's tackle this problem step by step. we have to find the sum of all integers from 0 to 9999 incl(...TRUNCATED)
"[{'start': 1, 'end': 2, 'description': 'Problem setup and initial understanding of requirements', '(...TRUNCATED)
"section1: Let's tackle this problem step by step. we have to find the sum of all integers from 0 to(...TRUNCATED)
"[{'section_number': 1, 'strategy_shift': '1', 'strategy_shift_step': '1', 'reasoning_usefulness': '(...TRUNCATED)
0
[1]
[4]
[4]
[2]
End of preview. Expand in Data Studio

OpenStellarTeam/DeltaBench(複製)

データの内容

o1 系の推論モデルが生成した長い思考連鎖(CoT)の誤りを、批評モデルや PRM が検出できるかを評価するためのデータ。数学・プログラミング・物理化学生物(PCB)・一般推論の千件余りのサンプルで、1 行が問題と長い CoT 1 件であり、各セクションに戦略の転換・推論の有用性・推論の正しさ(最初の誤り、説明、訂正)・内省の効率のラベルが付いている。調査メモでは評価向けで学習には件数が小さいとされ、カードは学習・研究向けのラベル付きデータを後で公開する予定としている。

データの概要

項目 値
行数 1,236(1 構成・1 分割の合計)
列数 16
容量 63.60 MB(ファイル 3 本)
ファイルの形式 csv 1
公開 public

構成と分割

構成(config) 分割(split)ごとの行数 列数
default train 1,236 16

列(構成 default・分割 train)

列 型 先頭の行の値
id string f11c7a6bbf5754fee116b638d99a33a6
origin string Omni-MATH_pascal
task_l1 string math
task_l2 string Number Theory
question string We call the pair $(m, n)$ of positive integers a…
solution string Suppose that $(205800, 35k)$ is a happy pair. We…
answer string 30
long_cot string Let's tackle this problem step by step. we need …
sections string [{'start': 1, 'end': 3, 'description': 'Introduc…
sections_content string section1: Let's tackle this problem step by step…
sections_labeled_info string [{'section_number': 1, 'strategy_shift': '0', 's…
final_correct int64 0
stragegy_shift_section_numbers string [2]
reason_unuseful_section_numbers string []
reason_error_section_numbers string [7]
reflection_section_numbers string []

行数と列は HF のデータセットビューアの集計(元のデータセットの現在の版で数えたもの)。全データセットの一覧は HYUKI5/dataset-catalog にある。

複製について

OpenStellarTeam/DeltaBench をリビジョン 894d233e5beb06b312b29761cc10e10ca5d2588a の時点でそのまま複製したもの。中身は変えていない。判断モデル Laya(convaiinnovations/laya)の微調整に使う候補として、調査メモ(Laya 学習用データセット調査)に載せたデータを集めている。

出典

論文

アノテーションの方法

(元のカードに該当の見出しが無いので、ラベルの付け方に触れた段落を抜き出した)

DeltaBench は、o1 系のモデルが生成した長い CoT の質的な特徴を分析し、既存の批評モデルや PRM が、Detect Error in Long CoT ReAsoning(長い CoT 推論における誤りの検出)を行う能力を評価するための、最初のデータセットである。具体的には、DeltaBench は多様な領域にわたる 1,236 件のサンプルからなり、数学、プログラミング、PCB(物理・化学・生物)、一般推論を含む。各サンプルは、問題、それに対応する長い CoT の解答、そして包括的な人手のアノテーションを含む。

  • DeltaBench を紹介する。o1 系のモデルが生成した長い CoT の質的な特徴を分析し、既存の批評モデルと PRM が、長い CoT 推論における Detect Error in Long CoT ReAsoning を行う能力を評価する、最初のデータセットである。具体的には、DeltaBench では、さまざまな o1 系モデル(QwQ、DeepSeek-R1、Gemini-2.0 Flash Thinking など)が生成した多様な長い CoT を、数学、プログラミング、PCB(物理・化学・生物)、一般推論などの推論タスクにわたって収集する。 次に、各長い CoT を異なるセクションに分割する。各セクションは独立したサブタスクを表す。

  • 1️⃣戦略の転換: このセクションが新しい手法や戦略の試みを導入しているかどうか。新しい戦略を導入している場合は、その具体的なステップをアノテーションする。

  • 2️⃣推論の有用性: このセクションの推論が有用かどうか。

  • 3️⃣推論の正しさ: このセクションに誤りが含まれるかどうか。誤りがある場合は、誤りが最初に現れるステップ番号、説明、訂正を含む、誤りに関する追加のフィールドをアノテーションする。

  • 4️⃣内省の効率(Reflection Efficiency): このセクションに内省(リフレクション)が含まれるかどうか、そして内省が正しいかどうか。内省がある場合は、内省が始まるステップをアノテーションする。

微調整に使うときの注意

  • 調査メモの台帳での区分: D(記載なし・other・unknown・資料間の食い違い)。区分は記載の文言で機械的に付けたもので、法的な判定ではない。学習に入れる前に元のカードとライセンスの原文で確かめる。
  • Laya の入力は 2,048 token まで(ModernBERT-large / mmBERT)。長い本文は先頭から黙って切られるので、切れる行は事前に除くか、要約・切り出しをしてから入れる。
  • 分割は記事・文書単位で行い、同じ本文から作った別の問いを学習側と較正側に分けない。温度と閾値は学習に使っていない分割で別々に当てる。

調査メモの記述

メモ 節 ライセンス(記載) 確認 注記
reasoning_process_labels.md Q2. 推論の誤りの「位置・種類・理由」を人手で付けた検出ベンチは何があるか(数学以外を含む) (L57) HF の license 欄は None。GitHub 側は未確認 未確認 原文注記: 件数 1,236 は評価向けで、学習には小さい。長さは下の Inferences。general(147 件)は論理・記号・数量・戦略・常識推論で、金融の論述とは別

元のカード(日本語訳)

以下は元のデータセットのカードの本文を日本語に訳したもの(機械翻訳)。訳に疑問があるときは、末尾の原文を確かめる。


概要

🌐 ウェブサイト • 🤗 Hugging Face • ⏬ データ • 📃 論文 • 🖥️ Github

💥 DeltaBench

DeltaBench は、o1 系のモデルが生成した長い CoT の質的な特徴を分析し、既存の批評モデルや PRM が、Detect Error in Long CoT ReAsoning(長い CoT 推論における誤りの検出)を行う能力を評価するための、最初のデータセットである。具体的には、DeltaBench は多様な領域にわたる 1,236 件のサンプルからなり、数学、プログラミング、PCB(物理・化学・生物)、一般推論を含む。各サンプルは、問題、それに対応する長い CoT の解答、そして包括的な人手のアノテーションを含む。

詳細は、ウェブサイト または 論文 を参照。

🆕 ニュース

  • [近日公開] ラベル付きのデータセットを今後さらに公開する予定である。学習・研究用途に利用できるようになる予定である。続報に注目 🔥🔥🔥

  • [2025.03.05] DeltaBench データセットを 🤗huggingface で公開した 🚀🚀🚀。

💫 導入

  • DeltaBench を紹介する。o1 系のモデルが生成した長い CoT の質的な特徴を分析し、既存の批評モデルと PRM が、長い CoT 推論における Detect Error in Long CoT ReAsoning を行う能力を評価する、最初のデータセットである。具体的には、DeltaBench では、さまざまな o1 系モデル(QwQ、DeepSeek-R1、Gemini-2.0 Flash Thinking など)が生成した多様な長い CoT を、数学、プログラミング、PCB(物理・化学・生物)、一般推論などの推論タスクにわたって収集する。 次に、各長い CoT を異なるセクションに分割する。各セクションは独立したサブタスクを表す。

​ その後、各セクションには次のタグが付与される:

  • 1️⃣戦略の転換: このセクションが新しい手法や戦略の試みを導入しているかどうか。新しい戦略を導入している場合は、その具体的なステップをアノテーションする。
  • 2️⃣推論の有用性: このセクションの推論が有用かどうか。
  • 3️⃣推論の正しさ: このセクションに誤りが含まれるかどうか。誤りがある場合は、誤りが最初に現れるステップ番号、説明、訂正を含む、誤りに関する追加のフィールドをアノテーションする。
  • 4️⃣内省の効率(Reflection Efficiency): このセクションに内省(リフレクション)が含まれるかどうか、そして内省が正しいかどうか。内省がある場合は、内省が始まるステップをアノテーションする。

📊 リーダーボード

詳細は 📊 を参照。

📜 引用

本データセットを利用する場合は、論文を引用してほしい。

@misc{he2025largelanguagemodelsdetect,
      title={Can Large Language Models Detect Errors in Long Chain-of-Thought Reasoning?}, 
      author={Yancheng He and Shilong Li and Jiaheng Liu and Weixun Wang and Xingyuan Bu and Ge Zhang and Zhongyuan Peng and Zhaoxiang Zhang and Zhicheng Zheng and Wenbo Su and Bo Zheng},
      year={2025},
      eprint={2502.19361},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2502.19361}, 
}
原文(英語)

Overview

🌐 Website • 🤗 Hugging Face • ⏬ Data • 📃 Paper • 🖥️ Github

💥 DeltaBench

DeltaBench the first dataset to analyze the qualities of the long CoTs generated by o1-like models and evaluate the critique abilities to Detect Error in Long CoT ReAsoning of existing critic models and PRMs. Specifically, DeltaBench comprises 1,236 samples across diverse domains, including Math, Programming, PCB (physics, chemistry and biology), and General Reasoning. Each sample encompasses a problem, its corresponding long CoT solution, and comprehensive human annotations

Please visit our website or check our paper for more details.

🆕 News

  • [Soon] We plan to release more of our labeled datasets, which will be available for training and research purposes. Stay tuned 🔥🔥🔥

  • [2025.03.05] We have released the DeltaBench dataset 🤗huggingface 🚀🚀🚀.

💫 Instroduction

  • we introduceDeltaBench, the first dataset to analyze the qualities of the long CoTs generated by o1-like models and evaluate the critique abilities to Detect Error in Long CoT ReAsoning of existing critic models and PRMs. Specifically, in DeltaBench, we first collect a diverse collection of long CoTs generated by various o1-like models (i.e., QwQ, DeepSeek-R1, and Gemini-2.0 Flash Thinking) across different reasoning tasks such as Math, Programming, PCB (physics, chemistry and biology), and General Reasoning. Then, we divide each long COT into different sections, where each section denotes an independent subtask.

​ After that, each section includes the following tags:

  • 1️⃣Strategy Shift: whether this section introduces a new method or strategy attempt. If a new strategy is introduced, the specific step is annotated.
  • 2️⃣Reasoning Usefulness: whether the reasoning in this section is useful.
  • 3️⃣Reasoning Correctness: whether this section contains any errors. If an error is present, additional error-related fields are annotated, including the first step number at which the error occurs, explanation and correction.
  • 4️⃣Reflection Efficiency: whether this section contains reflection and whether the reflection is correct. If reflection is present, the step at which the reflection begins is annotated.

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📜 Citation

Please cite our paper if you use our dataset.

@misc{he2025largelanguagemodelsdetect,
      title={Can Large Language Models Detect Errors in Long Chain-of-Thought Reasoning?}, 
      author={Yancheng He and Shilong Li and Jiaheng Liu and Weixun Wang and Xingyuan Bu and Ge Zhang and Zhongyuan Peng and Zhaoxiang Zhang and Zhicheng Zheng and Wenbo Su and Bo Zheng},
      year={2025},
      eprint={2502.19361},
      archivePrefix={arXiv},
      primaryClass={cs.CL},
      url={https://arxiv.org/abs/2502.19361}, 
}
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